Operations Research:

This area of mathematics came into existence during World War II. It uses mathematics (primarily linear algebra and probability/statistics) to solve problems that occur in business and managerial situations.

Game theory, a part of operations research, was used to select a strategy for the Battle of Midway, a turning point in the Pacific arena during World War II. The U.S. Navy was on one side of Midway Island, and the Japanese Navy on the other. We calculated our probability of winning in the four cases of our going north of the island or south of it, and the same for the Japanese. Game theory was then used to select the winning strategy.

Linear programming (the other major part of operations research) was also used at the start of the war to determine how many of our pilots (we had very few) should be used to fight in the war and how many to train other pilots.